634 BELL SYSTEM TECIIXICAL JOURNAL 



Inside of the beam the effect of the electrons is to change the effective 

 dielectric constant in the z direction. Thus, from (2.22) we have for the elec- 

 tron convection current 



• - 2Foaft - r)= ^^^^ 



Now 



£. = - ^ = rF (14.6) 



so that 



' 2Fo(y/3. - r)^ ^^^-'^ 



The appearance of a voltage V in (2.22) and (14.6) does not mean that these 

 relations are invalid for fast waves. In (2.22) the only meaning which need 

 be given to V is that defined by (14.6), as it is the electric field as specified 

 by (14.6) that was assumed to act on the electrons in deriving (2.22). 

 Let us say that the total a-c current density in the z direction, Jz , is 



Jz = jo}tiEz (14.8) 



This current consists of a displacement current jcoeE^ and the current i, 

 so that 



Hence 



\ 2ecoFo(;/3e- 1)7 



This gives the ratio of the effective dielectric constant in the z direction to 

 the actual dielectric constant. We will proceed to put this in a form which 

 in the long run will prove more convenient. 

 Let us define a quanity (3 



(14.11) 

 (14.12) 



(14.13) 

 (14.14) 



\ 



